Network Analysis and the Humanities

16 June 2021

Networks are everywhere.. but what are they?

We live in a ‘networked world’
The word ‘network’ is ubiquitous:
- Communication networks
- Transport networks
- Social networks
Has a formal meaning in mathematics, social and physical sciences: a representation of the relations between entities

You don’t have to look to hard to see networks everywhere. In fact, you probably use the term network every day without thinking about it. It has come to have a very general meaning of a system, usually complex, of interconnected things. In the news we hear talk of shutting down networks of terrorist cells. There are communication networks, like the network of fiber-optic cables found under the sea, as seen here, and transport networks, like the London tube. We are constantly told that everything is connected, or that it should be by everyone from politicians to advertisers.

But the term network also has a more formal meaning in the fields of mathematics and physical and social sciences. It is the name for a mathematical object, of things and the relations between them, represented as a graph of nodes and edges.

You might wonder how this applies to humanities subjects such as the study of the past, or literature, and so forth. But what I want to suggest to you is that in fact almost anything can be represented and analysed as a network, and it is a powerful and useful metaphor for thinking about any range of subjects.

Goals of this lecture

The lecture will be a brief overview of the origins and concept of network analysis as it applies to humanities subjects.
By the end you should:
- Have a basic knowledge of network analysis and its key concepts
- Understand key terminology such as nodes and edges
- Understand some important network measurements and how to interpret them
- Have a practical starting-point for the tools and methods needed to turn your own research into network data

Leonard Euler, graph theory, and the ‘Königsberg Bridge Problem’

Network analysis has its origins in ‘graph theory’, put forward by the 18th-century mathematician Leonhard Euler.
Trying to solve the ‘Königsberg Bridge problem’

The idea of representing complex systems as a ‘graph’ actually goes back to the 18th century, and the mathematician Leonhard Euler. The legend is that Euler was interested in a puzzle known as the Koningsberg Bridge Problem. The town of Koningsberg was built on two islands in the middle of the Preger River, and joined to each other and the river banks by seven bridges. Residents of the town wondered if it was possible to walk a route around the town which would touch all parts of land and cross each bridge exactly once.

Euler was able to solve the problem by transforming the town into an abstract diagram, known as a ‘graph’. In this graph, the landmasses were called ‘nodes’, or vertices, and the bridges called edges. With this simplified model, Euler was able to develop a series of mathematical rules. One of these said that if more than two nodes (landmasses) had an odd number of edges (bridge), it was impossible to draw a path which touched each once, and therefore proved that it was impossible to draw the walking route described above.

From Graphs to Networks…

Graphs can be used to represent networks of ‘things’ (called nodes) and connections between them (called links or edges).
Often represented as a ’network diagram, where the nodes are points and the edges lines.
They have a few additional properties: they can be directed and weighted

Directed Networks

Directed networks are ones in which the information flows in a particular direction, from one node to another.

Weighted Networks

A weighted network is one where these is a measurement representing the strength of the ties between the nodes.

Bipartite Networks

Nodes can be of more than one type, for example a network of actors connected to movie genres
Known as bipartite or bimodal if there are two types
Need additional steps to be analysed in the same way as ‘regular’ networks

Another type of network is one where the nodes are not all the same type, say people or cities, but the connections are between completely different things. It could be a network of people connected to the companies they work for, predators connected to their prey in an ecological network, for example. If there are two types, it is known as a bi-partite network. Here, I drew a network of actors connected to movie genres. The resulting network diagram shows how different genres cluster together based on the actors who act in them: you can see here that the action, crime and horror genres are clustered together because they share a similar group of actors, and comedy, romance and drama are clustered separately. Often these bipartite networks need additional steps or different sets of metrics in order to analyse them, but they are very often found in humanities data.

Social Network Analysis

Degree

Counts the number of connections to a particular node
Can be directed and weighted

Directed Degree

Weighted Degree

Betweenness centrality

First an algorithm calculates all the ‘shortest paths’ from every pair of nodes.
A node scores highly for betweenness centrality if it is used on many of these paths

Eigenvector centrality

Measures importance through a node’s connection to other important nodes
Similar to the ‘PageRank’ system used by Google to rank search results by importance.

The "New Science of Networks’

Using network theory to understand and map very large complex systems such as the internet
Papers by Barabasi (1999) and Watts & Strogatz (1998) shows that many real-world networks have a similar structure
A small number of nodes with many connections, often called ‘hubs’, and many nodes with very few connections.

The next big revolution in network analysis came in the 1990s. Inspired by the complexity of the internet, scientists and mathematicians realised that network analysis could be used to map and understand huge and extraordinarily complex systems. In landmark papers written at the turn of the millennium, researchers using network theory showed that many of these large, real-world networks shared a similar structure. Rather than being randomly distributed, so that some nodes have fairly similar number of connections, they found that many, perhaps most networks have a small number of hubs with a huge number of connections, and a large number of nodes with very few connections. On twitter, for example, there are a small number of Kim Kardashians and Barack Obamas with millions of followers, and then millions of people like me, with a tiny number of followers. This is an example from my own research looking at a network made from almost half a million letter records: you can see that there are a number of very important hubs, the largest-sized nodes, connected to lots of smaller-sized nodes.

A ‘Small-world’

Hubs make it easy to reach other parts of network even with a very few total connections
This has been called the ‘small-world’ phenomenon, and helps to explain why everyone is so well-connected to everyone else!
These types of networks are also resistant to failure but susceptible to targeted attack.

This discovery has formed the basis for a new science of networks. These hubs make it much quicker than expected to get across a network. In a scale-free network, the quickest way to get to any other node is often to travel first to a hub, because it’s very like that they will have a direct connection: think of it like travelling by airplane. It would be very inefficient and slow if every city was connected to every other one by a direct flight. Rather we fly to a big international airport first and go from there. This has been called the ‘small-world’ phenomenon, and it perhaps goes some way to explaining how well connected everything is: you don’t need to know everyone, just a couple of important hubs.

Researchers found that these scale-free networks also have a bunch of other interesting properties. For example, they are resistant to random failure - because its unlikely that the hubs will be accidentally taken out, but sensitive to targeted attack, if you can target a highly-connected node. The same network shape can be found across lots of different fields and types of networks. In my own work I have constructed networks of news centres, where the nodes are cities, and correspondence networks, where the nodes are letter-writers, and in both cases also found this scale-free structure.

Network Analysis and the Humanities

Networks particularly suitable to humanities data, because we are in the business of relations
In the past 20 years has been used to analyse historical social networks, archaeology, geographic networks, historical infrastructure, and others
Also relevant to many other areas: even literary studies, art history etc.

Since these landmark studies, academic interest in networks has exploded. In the last 20 years researchers have represented all sorts of systems as complex networks. Humanities are particularly suited to networks because so much of our data is about relations of some kind. As well as historical social networks, using relationships or correspondence data, it’s been used in archaeology, for example Paul Arthur and others have drawn networks based on shared pottery styles found in archaeological digs.

So far, we’ve talked about letter networks, archaeological networks, communication networks such as roads or postal systems, and social relations between people. You might be thinking, as a digital humanities scholar I am interested in something far less structured: text analysis, analysing literature at scale, art history, and so forth. How on earth might this apply to my own research?

Almost anything can be a network..

Almost anything can be represented as a network
Network of words in a literary text, or characters in a play
http://www.martingrandjean.ch/network-visualization-shakespeare/

The fact is, while we often think of ‘network analysis’ in terms of ‘social network analysis’, because it’s the most commonly known these days, network analysis is suitable for gaining insight into any kind of data that is in some way relational - that is, the pieces of data can be said to be in some way interrelated. Firstly, networks do not have to be based on real people. Martin LeGrandJean has visualised Shakespeare plays as social networks, drawing links between the characters every time they appear in the same scene together. The resulting networks helps us to understand how the characters are interrelated, and using a measurement known as density, are able to give an overall sense of the complexity of each play. LeGrandjean showed that a play like Hamlet, though longer, was less structurally complex than King Lear, for example.

I encourage you to think outside the box, and consider how your own area of interest, perhaps a disseration topic or essay, could be represented as a network. For example, researchers have constructed networks of words which co-occur in the same novel together. The resulting network can be analysed in the same way as any other network, looking for the most centrally-placed words, or looking for clusters of words which appear together often. This might highlight key themes or subjects within a novel, or help to understand the writing style of an author. The connections might be very abstract: the similarity between two paintings in terms of colour, for example, or what is known as a ‘line of sight’ network in archaeology, where a link is drawn if one settlement can directly see another.

Networks of cities..

In my own research I made a ‘social network of cities’ based on news transmission
Network data was collected from printed news sources
Needed extensive correction and manual cleaning

Constructing and Analysing Network Data: practical steps

Networks very commonly constructed from an ‘edge list’: a list of connections between pairs of nodes, often in a simple spreadsheet with two columns
Data can be entered manually on a small scale
Lots of existing humanities datasets available online, ready for network analysis.
A huge range of software out there to visualise and analyse, for all levels of expertise.

Once you have established something as nodes and edges in your research data, there are a number of ways to analyse it. This week’s assignment walks through turning a collection of historical letters into network data. I won’t go into too much detail as the instructions are quite detailed, but the easiest way to construct a network is by making an ‘edge list’: a list of pairs of connected nodes. There are also lots of ready-made datasets freely available online, and I would encourage you to do some research as your area of interest might already have a relevant dataset ready to go.

This can be inputted to a web application such as Network Navigator, used in this week’s assignment, software such as Gephi, or, if you have some programming experience, a package such as NetworkX in Python or Igraph in R.

Network Visualisation

Often represented as a force-directed network
Highly-connected groups of nodes are placed closely together
Useful to get a sense of the overall ‘topology’, or map of a network, findings its centres, peripheries and separate clusters

Once you have constructed and uploaded you network, you have a number of options for analysing it. The first is visual. Many of these programmes will visualise your network data as what is known as a force-directed diagram. In a force-directed diagram, closely-connected nodes are put together, and generally the most-connected nodes end up towards the centre. The resulting visualisation can be really useful, quickly showing you the clusters, the centres and peripheries, and how different parts of the network are related to each other. In the example of the news network, shown above, this allow me to see that Paris and den Haag, despite not being the most-connected, were the most central to the network overall, and that there were some interesting clusters, including Madrid and Genoa which despite being far apart geographically, were linked politically and by shared news.

Network Analysis Metrics

The metrics above can be used to highlight important nodes
Think about the implications of each one for your own data and research
For example high degree score in historical social network might indicate an important communicator; high degree in an archaeological network something else entirely.

Pitfalls of Network Analysis

Be careful in interpreting the results - particularly with messy data
How might your data ‘cleaning’ impact your findings?
To what extent are findings the result of collection or archival practices?
Some network types (such as bipartite) need additional steps before they can be analysed correctly

In the assignment that you will do for this week, you’ll see that the data is not straightforward. First, you need to decide what in the data you will represent as a network - meaning that you as the researcher have to do some kind of interpretation. You will also notice that the information isn’t perfect: there are spelling mistakes and inconsistencies, which will have an effect on the computational analysis. I would encourage you to think about how this might impact your findings, and consider the extent to which findings are the result of decisions taken by you as the researcher. Consider also the data itself - is it free from bias? To what extent does the network reflect the data, or the way it has been collected or archives? Lastly, not all networks are the same, and some, like bipartite networks, where the nodes are of different types, need additional steps before they can be analysed correctly

Conclusions

Networks can be a powerful way to quantitatively assess related objects
Easy to analyse with a variety tools
Both visualisation and network metrics can be useful
Think about how your own data might be represented as a network